Full characterization of Airy beams under physical principles

The propagation characteristics of Airy beams is investigated and fully described under the traveling-wave approach analogous to that used for nondiffracting Bessel beams. This is possible when noticing that Airy functions are, in fact, Bessel functions of fractional order 1/3. We show how physical principles impose restrictions such that the nondiffracting Airy beams cannot be of infinite extent as has been argued and introduce quantitative expressions for the maximum transverse and longitudinal extent of Airy beams. We show that under the appropriate physical conditions it is possible to obtain higher-order Airy beams.